Honeycomb filter structures for DPF (Diesel Particulate Filters) are widely known in the conventional art. Such honeycomb filter structures are produced by using a plugging material to plug one sides of some of the through-holes of a green molded body produced with an extruder, while plugging the other sides of the other through-holes with a plugging material, and firing the structure. Patent literature 1 discloses a continuous heating furnace used for production of ceramic products.